涡量方程 （英語：vorticity equation ）是流体力学 中描述流体 质点涡量 变化的方程。可压缩牛顿流体 的涡量方程表达式为：
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{\displaystyle {\begin{aligned}{\frac {D{\boldsymbol {\omega }}}{Dt}}&={\frac {\partial {\boldsymbol {\omega }}}{\partial t}}+(\mathbf {u} \cdot \nabla ){\boldsymbol {\omega }}\\&=({\boldsymbol {\omega }}\cdot \nabla )\mathbf {u} -{\boldsymbol {\omega }}(\nabla \cdot \mathbf {u} )+{\frac {1}{\rho ^{2}}}\nabla \rho \times \nabla p+\nabla \times \left({\frac {\nabla \cdot \tau }{\rho }}\right)+\nabla \times \left({\frac {B}{\rho }}\right)\end{aligned}}}
其中D / Dt 物质导数 ，u 流速 ，ρ 密度 ，p 压强 ，τ 粘性应力张量 ，B 涡旋伸展 。使用爱因斯坦求和约定 指标记号，上式又可写作
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{\displaystyle {\begin{aligned}{\frac {d\omega _{i}}{dt}}&={\frac {\partial \omega _{i}}{\partial t}}+v_{j}{\frac {\partial \omega _{i}}{\partial x_{j}}}\\&=\omega _{j}{\frac {\partial v_{i}}{\partial x_{j}}}-\omega _{i}{\frac {\partial v_{j}}{\partial x_{j}}}+e_{ijk}{\frac {1}{\rho ^{2}}}{\frac {\partial \rho }{\partial x_{j}}}{\frac {\partial p}{\partial x_{k}}}+e_{ijk}{\frac {\partial }{\partial x_{j}}}\left({\frac {1}{\rho }}{\frac {\partial \tau _{km}}{\partial x_{m}}}\right)+e_{ijk}{\frac {\partial B_{k}}{\partial x_{j}}}\end{aligned}}}
对于保守外力 作用下的不可压缩流体 ，涡量方程可以简化为
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{\displaystyle {\frac {D{\boldsymbol {\omega }}}{Dt}}=\left({\boldsymbol {\omega }}\cdot \nabla \right)\mathbf {u} +\nu \nabla ^{2}{\boldsymbol {\omega }}}
其中ν 运动黏度 ，∇2 拉普拉斯算符 。
参考文献 Manna, Utpal; Sritharan, S. S. Lyapunov Functionals and Local Dissipativity for the Vorticity Equation in LTemplate:Isup 20 (5): 581–598. Barbu, V.; Sritharan, S. S. M (PDF) . Balakrishnan, A. V. (编). Semi-Groups of Operators: Theory and Applications. Boston: Birkhauser. 2000: 296–303 [2016-12-10 ] . （原始内容存档 (PDF) 于2016-03-03）. Krigel, A. M. Vortex evolution. Geophysical, Astrophysical Fluid Dynamics. 1983, 24 : 213–223. 
